Details

sample23.0ms

Algorithm

intervals

Results

12.0ms

256×

body

valid

simplify16.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	16	7
1	27	7
2	33	7
3	34	7
4	34	7

prune3.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 38.9b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (+ (* x x) (* y y)) (* z z))
0.3b	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
35.8b	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
19×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
13×	`sqrt-prod`
8×	`add-log-exp`
5×	`add-exp-log` `add-cbrt-cube`
4×	`pow1`
3×	`expm1-log1p-u` `fma-def` `associate-/r` `sum-log` `log1p-expm1-u` `associate-/l`
2×	`rem-sqrt-square` `flip3-+` `flip-+` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `associate-+l+` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `div-exp` `clear-num`

Counts

3 → 76

Calls

3 calls:

7.0ms	(+ (+ (* x x) (* y y)) (* z z))
11.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
7.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

series282.0ms

Counts

3 → 9

Calls

3 calls:

38.0ms	(+ (+ (* x x) (* y y)) (* z z))
59.0ms	(/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)
185.0ms	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0))

simplify143.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 3 (133.0ms)

Iter	Nodes	Cost
0	272	784
1	1063	695
2	4582	674
3	5001	673

prune261.0ms

Filtered

85 candidates to 71 candidates (83.5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	79	6	85
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	80	6	86

Merged error: 19.3b

Counts

86 → 6

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (+ (* x x) (* y y)) (* z z))
0.4b	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
36.0b	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

45×	`sqrt-prod`
36×	`times-frac`
35×	`add-sqr-sqrt`
33×	`add-cube-cbrt` `*-un-lft-identity`
8×	`add-log-exp`
6×	`associate-/r` `associate-/l`
5×	`add-exp-log` `add-cbrt-cube`
4×	`pow1` `sqrt-div`
3×	`expm1-log1p-u` `fma-def` `flip3-+` `sum-log` `flip-+` `log1p-expm1-u`
2×	`associate-/l/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `associate-+l+` `sqrt-undiv` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `hypot-def` `div-inv`

Counts

3 → 101

Calls

3 calls:

7.0ms	(+ (+ (* x x) (* y y)) (* z z))
10.0ms	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
6.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

series395.0ms

Counts

3 → 9

Calls

3 calls:

40.0ms	(+ (+ (* x x) (* y y)) (* z z))
239.0ms	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3.0))
116.0ms	(sqrt (+ (+ (* x x) (* y y)) (* z z)))

simplify142.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	275	1280
1	1042	1198
2	4966	1164
3	5001	1164

prune246.0ms

Filtered

110 candidates to 73 candidates (66.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	106	4	110
Fresh	0	5	5
Picked	1	0	1
Done	0	0	0
Total	107	9	116

Merged error: 15.7b

Counts

116 → 9

localize10.0ms

Local error

Found 2 expressions with local error:

0.4b	(/ (hypot (sqrt (+ (* x x) (* y y))) z) (sqrt 3.0))
32.7b	(sqrt (+ (* x x) (* y y)))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt`
18×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
15×	`sqrt-prod`
6×	`associate-/r*`
4×	`add-exp-log` `add-cbrt-cube`
3×	`pow1` `associate-/l*`
2×	`expm1-log1p-u` `sqrt-div` `log1p-expm1-u` `add-log-exp`
1×	`cbrt-undiv` `rem-sqrt-square` `sqrt-undiv` `hypot-udef` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `div-exp` `clear-num` `flip-+` `hypot-def` `div-inv`

Counts

2 → 60

Calls

2 calls:

5.0ms	(/ (hypot (sqrt (+ (* x x) (* y y))) z) (sqrt 3.0))
4.0ms	(sqrt (+ (* x x) (* y y)))

series342.0ms

Counts

2 → 6

Calls

2 calls:

299.0ms	(/ (hypot (sqrt (+ (* x x) (* y y))) z) (sqrt 3.0))
42.0ms	(sqrt (+ (* x x) (* y y)))

simplify111.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 2 (19.0ms)

Iter	Nodes	Cost
0	211	654
1	555	614
2	1415	600
3	3989	600
4	5002	600

prune181.0ms

Filtered

66 candidates to 49 candidates (74.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	63	3	66
Fresh	3	5	8
Picked	1	0	1
Done	0	0	0
Total	67	8	75

Merged error: 0.1b

Counts

75 → 8

localize7.0ms

Local error

Found 1 expressions with local error:

0.4b	(/ (hypot (hypot x y) z) (sqrt 3.0))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

18×	`times-frac`
16×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
12×	`sqrt-prod`
6×	`associate-/r*`
3×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
1×	`pow1` `cbrt-undiv` `expm1-log1p-u` `sqrt-undiv` `hypot-udef` `frac-2neg` `div-exp` `clear-num` `log1p-expm1-u` `div-inv` `add-log-exp`

Counts

1 → 42

Calls

1 calls:

4.0ms

(/ (hypot (hypot x y) z) (sqrt 3.0))

series324.0ms

Counts

1 → 3

Calls

1 calls:

324.0ms

(/ (hypot (hypot x y) z) (sqrt 3.0))

simplify66.0ms

Algorithm

egg-herbie

Counts

45 → 45

Iterations

Useful iterations: 4 (60.0ms)

Iter	Nodes	Cost
0	123	356
1	301	338
2	762	327
3	2096	327
4	5001	326

prune103.0ms

Filtered

45 candidates to 31 candidates (68.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	41	4	45
Fresh	6	1	7
Picked	0	1	1
Done	0	0	0
Total	47	6	53

Merged error: 0b

Counts

53 → 6

regimes117.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	8	4

end0.0ms

sample557.0ms

Algorithm

intervals

Results

377.0ms

8000×

body

valid